We have carried out high-precision timing measurements of the binary
millisecond pulsar PSR J2051-0827 with the Effelsberg 100-m radio telescope
of the Max-Planck-Institut für Radioastronomie and with the
Lovell 76-m radio telescope at Jodrell Bank. The 6.5-yrs radio timing
measurements have revealed a significant secular variation of the
projected semi-major axis of the pulsar at a rate of , which is probably
caused by the Newtonian spin-orbit coupling in this binary system
leading to a precession of the orbital plane. The required
misalignment of the spin and orbital angular momenta of the companion
are evidence for an asymmetric supernova explosion.
We have also confirmed that the orbital period is currently decreasing at
a rate of s s-1
and have measured second and third orbital period derivatives and , which indicate a quasi-cyclic
orbital period variation similar to those found in another eclipsing
pulsar system, PSR B1957+20. The observed variation of the
orbital parameters constrains the maximal value of the companion
radius to
and implies that the companion is underfilling its Roche lobe by 50% .
The derived variation in the quadrupole moment of the companion
is probably caused by tidal dissipation similar to the mechanism
proposed for PSR B1957+20. We conclude that the companion is at
least partially non-degenerate, convective and magnetically active.

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